Bulletin of Mathematical Biology

, Volume 76, Issue 5, pp 1117–1142 | Cite as

Athero-protective Effects of High Density Lipoproteins (HDL): An ODE Model of the Early Stages of Atherosclerosis

  • Anna Cohen
  • Mary R. Myerscough
  • Rosemary S. Thompson
Original Article


We present an ODE model which we use to investigate how High Density Lipoproteins (HDL) reduce the inflammatory response in atherosclerosis. HDL causes atherosclerotic plaque stabilisation and regression, and is an important potential marker and prevention target for cardiovascular disease. HDL enables cholesterol efflux from the arterial wall, macrophage and foam cell emigration, and has other athero-protective effects. Our basic inflammatory model is augmented to include several different ways that HDL can act in early atherosclerosis. In each case, the action of HDL is represented via a parameter in the model. The long-term model behaviour is investigated through phase plane analysis and simulations. Our results indicate that only HDL-enabled cholesterol efflux can stabilise the internalised lipid content in the lesion so that it does not continue to grow, but this does not reduce macrophage numbers which is required to stabilise the lesion or prevent rupture. HDL-enabled macrophage emigration guarantees lesion stabilisation by maintaining stable macrophage content.


Cardiovascular disease Dynamical systems 


  1. Aicher, B. O., Haser, E. K., Freeman, L. A., Carnie, A. V., Stonik, J. A., Wang, X., Remaley, A. T., Kato, G. J., & Canon, R. O. III (2012). Diet-induced weight loss in overweight or obese women and changes in high-density lipoprotein levels and function. Obesity, 20(10), 2057–2062. CrossRefGoogle Scholar
  2. Ameli, S., Hultgardh-Nilsson, A., Cercek, B., Shah, P. K., Forrester, J. S., Ageland, H., & Nilsson, J. (1994). Recombinant apolipoprotein A-I Milano reduces intimal thickening after balloon injury in hypercholesterolemic rabbits. Circulation, 90(4), 1935–1941. CrossRefGoogle Scholar
  3. Barter, P. J., Nicholls, S., Rye, K.-A., Anantharamaiah, G., Navab, M., & Fogelman, A. M. (2004). Anti-inflammatory properties of HDL. Circ. Res., 95(8), 764–772. CrossRefGoogle Scholar
  4. Berrougui, H., Isabelle, M., Cloutier, M., Grenier, G., & Khalil, A. (2007). Age-related impairment of HDL-mediated cholesterol efflux. J. Lipid Res., 48(2), 328–336. CrossRefGoogle Scholar
  5. Cobbold, C. A., Sherratt, J. A., & Maxwell, S. R. J. (2002). Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach. Bull. Math. Biol., 64, 65–95. CrossRefGoogle Scholar
  6. Dansky, H. M., & Fisher, E. A. (1999). High-density lipoprotein and plaque regression: the good cholesterol gets even better. Circulation, 100(17), 1762–1763. CrossRefGoogle Scholar
  7. Duffy, D., & Rader, D. J. (2006). Emerging therapies targeting high-density lipoprotein metabolism and reverse cholesterol transport. Circulation, 113(8), 1140–1150. CrossRefGoogle Scholar
  8. Ellison, R. C., Zhang, Y., Qureshi, M. M., Knox, S., Arnett, D. K., & Province, M. A. (2004). Lifestyle determinants of high-density lipoprotein cholesterol: the National Heart, Lung, and Blood Institute Family Heart Study. Am. Heart J., 147(3), 529–535. CrossRefGoogle Scholar
  9. Eriksson, M., Carlson, L. A., Miettinen, T. A., & Angelin, B. (1999). Stimulation of fecal steroid excretion after infusion of recombinant proapolipoprotein A-I. Circulation, 100(6), 594–598. CrossRefGoogle Scholar
  10. Feig, J. E., Rong, J. X., Shamir, R., Sanson, M., Vengrenyuk, Y., Liu, J., Rayner, K., Moore, K., Garabedian, M., & Fisher, E. A. (2011). HDL promotes rapid atherosclerosis regression in mice and alters inflammatory properties of plaque monocyte-derived cells. Proc. Natl. Acad. Sci. USA, 108(17), 7166–7171. CrossRefGoogle Scholar
  11. Hansson, G. K., & Libby, P. (2006). The immune response in atherosclerosis: a double-edged sword. Nat. Immunol., 6, 508–519. CrossRefGoogle Scholar
  12. Joy, T., & Hegele, R. (2008). Is raising HDL a futile strategy for atheroprotection?. Nat. Rev. Drug Discov., 7, 143–155. CrossRefGoogle Scholar
  13. Kennedy, M. A., Barrera, G. C., Nakamura, K., Baldan, A., Tarr, P., Fishbein, M. C., Frank, J., Francone, O. L., & Edwards, P. A. (2005). ABCG1 has a critical role in mediating cholesterol efflux to HDL and preventing cellular lipid accumulation. Cell Metabolism, 1, 121–131. CrossRefGoogle Scholar
  14. Kharbanda, R., & MacAllister, R. (2005). The atherosclerosis time-line and the role of the endothelium. Curr. Medicine Chem., 5, 47–52. Google Scholar
  15. Kunjathoor, V. V., Febbraio, M., Podrez, E. A., Moore, K. J., Andersson, L., Koehn, S., Rhee, J. S., Silverstein, R., Hoff, H. F., & Freeman, M. W. (2002). Scavenger receptors class A-I/II and CD36 are the principal receptors responsible for the uptake of modified low density lipoprotein leading to lipid loading in macrophages. J. Biol. Chem., 277(51), 49982–49988. CrossRefGoogle Scholar
  16. Lee, J. M., & Choudhury, R. P. (2007). Prospects for atherosclerosis regression through increase in high-density lipoprotein and other emerging therapeutic targets. Heart, 93, 559–564. CrossRefGoogle Scholar
  17. Lendon, C. L., Davies, M. J., Born, G. V. R., & Richardson, P. D. (1991). Atherosclerotic plaque caps are locally weakened when macrophages density is increased. Atherosclerosis, 87(1), 87–90. CrossRefGoogle Scholar
  18. Libby, P., & Ridker, P. M. (2006). Inflammation and atherothrombosis: from population biology and bench research to clinical practice. J. Am. Coll. Cardiol., 48, A33–A46. CrossRefGoogle Scholar
  19. Libby, P., Ridker, P. M., & Maseri, A. (2002). Inflammation and atherosclerosis. Circulation, 105, 1135–1143. CrossRefGoogle Scholar
  20. Linsel-Nitschke, P., & Tall, A. (2005). HDL as a target in the treatment of atherosclerotic cardiovascular disease. Nat. Rev. Drug Discov., 4, 193–205. CrossRefGoogle Scholar
  21. Liu, H., Shi, B., Huang, C.-C., Eksarko, P., & Pope, R. M. (2008). Transcriptional diversity during monocyte to macrophage differentiation. Immunol. Lett., 117(1), 70–80. CrossRefGoogle Scholar
  22. Llodrá, J., Angeli, V., Liu, J., Trogan, E., Fisher, E. A., & Randolph, G. J. (2004). Emigration of monocyte-derived cells from atherosclerotic lesions characterizes regressive, but not progressive plaques. Proc. Natl. Acad. Sci. USA, 101(32), 11779–11784. CrossRefGoogle Scholar
  23. Lusis, A. J. (2000). Atherosclerosis. Nature, 407, 233–241. CrossRefGoogle Scholar
  24. Morton, J., Bao, S., Celermajer, D. S., Ng, M. K., & Bursill, C. A. (2013). Strikingly different atheroprotective effects of apoliprotein A-I in early-stage versus late-stage atherosclerosis. Circulation, 128, A15785. Google Scholar
  25. Navab, M., Anantharamaiah, G., Reddy, S. T., Lenten, B. J. V., & Fogelman, A. M. (2009). HDL as a biomarker, potential therapeutic target, and therapy. Diabetes, 58(12), 2711–2717. CrossRefGoogle Scholar
  26. Nicholls, S. J. (2012). The aim-high (atherothrombosis intervention in metabolic syndrome with low HDL/high triglycerides: impact on global health outcomes) trial. To believe or not to believe? J. Am. Coll. Cardiol., 59(23), 2065–2067. CrossRefGoogle Scholar
  27. Nicholson, A. C., Han, J., Febbraio, M., Silverstein, R. L., & Hajjar, D. P. (2001). Role of CD36, the macrophage class B scavenger receptor, in atherosclerosis. Ann. N.Y. Acad. Sci., 947(1), 224–228. CrossRefGoogle Scholar
  28. Nissen, S. E., Tardif, J.-C., Nicholls, S. J., Revkin, J. H., Shear, C. L., Duggan, W. T., Ruzyllo, W., Bachinsky, W. B., Lasala, G. P., Tuzcu, E. M., & ILLUSTRATE Investigators (2007). Effect of torcetrapib on the progression of coronary atherosclerosis. N. Engl. J. Med., 356(13), 1304–1316. CrossRefGoogle Scholar
  29. Ougrinovskaia, A., Thompson, R. S., & Myerscough, M. R. (2010). An ODE model of early stages of atherosclerosis: mechanisms of the inflammatory response. Bull. Math. Biol., 72(6), 1534–1561. MathSciNetCrossRefMATHGoogle Scholar
  30. Parolini, G. C. C., & Marchesi, M. (2009). HDL therapy for the treatment of cardiovascular diseases. Curr. Vasc. Pharmacol., 7(4), 550–556. CrossRefGoogle Scholar
  31. Reis, E. D., Li, J., Fayad, Z. A., Rong, J. X., Hansoty, D., Aguinaldo, J.-G., Fallon, J. T., & Fisher, E. A. (2001). Dramatic remodeling of advanced atherosclerotic plaques of the apolipoprotein E-deficient mouse in a novel transplantation model. J. Vasc. Surg., 34(3), 541–547. CrossRefGoogle Scholar
  32. Rong, J. X., Li, J., Reis, E. D., Choudhury, R. P., Dansky, H. M., Elmalem, V. I., Fallon, J. T., Breslow, J. L., & Fisher, E. A. (2001). Elevating high-density lipoprotein cholesterol in apolipoprotein E-deficient mice remodels advanced atherosclerotic lesions by decreasing macrophage and increasing smooth muscle cell content. Circulation, 104(20), 2447–2452. CrossRefGoogle Scholar
  33. Ross, R. (1999). Atherosclerosis—an inflammatory disease. N. Engl. J. Med., 340, 115–126. CrossRefGoogle Scholar
  34. Singh, I. M., Shishehbor, M. H., & Ansell, B. J. (2007). High-density lipoprotein as a therapeutic target: a systematic review. JAMA J. Am. Med. Assoc., 298(7), 786–798. CrossRefGoogle Scholar
  35. Sirtori, C., & Fumagalli, R. (2006). LDL-cholesterol lowering or HDL-cholesterol raising for cardiovascular prevention: a lesson from cholesterol turnover studies and others. Atherosclerosis, 186, 1–11. CrossRefGoogle Scholar
  36. Soma, M. R., Donetti, E., Parolini, C., Sirtori, C. R., Fumagalli, R., & Franceschini, G. (1995). Recombinant apolipoprotein A-I Milano dimer inhibits carotid intimal thickening induced by perivascular manipulation in rabbits. Circ. Res., 76(3), 405–411. CrossRefGoogle Scholar
  37. Stary, H. C., Chandler, A. B., Glagov, S., Guyton, J. R., Insull, W., Rosenfeld, M. E., Schaffer, S. A., Schwartz, C. J., Wagner, W. D., & Wissler, R. W. (1994). A definition of initial, fatty streak and intermediate lesions of atherosclerosis—a report from the Committee on Vascular Lesions of the Council on Arteriosclerosis, American Heart Association. Circulation, 89(5), 2462–2478. CrossRefGoogle Scholar
  38. Thompson, P. D., & Rader, D. J. (2001). Does exercise increase HDL cholesterol in those who need it the most? Arterioscler. Thromb. Vasc. Biol., 21(7), 1097–1098. CrossRefGoogle Scholar
  39. Trogan, E., Feig, J. E., Dogan, S., Rothblat, G. H., Angeli, V., Tacke, F., Randolph, G. J., & Fisher, E. A. (2006). Gene expression changes in foam cells and the role of chemokine receptor CCR7 during atherosclerosis regression in ApoE-deficient mice. Proc. Natl. Acad. Sci. USA, 103(10), 3781–3786. CrossRefGoogle Scholar
  40. White, C., Datta, G., Zhang, Z., Gupta, H., Garber, D., Mishra, V., Palgunachari, M., Handattu, S., Chaddha, M., & Anantharamaiah, G. (2008). HDL therapy for cardiovascular diseases: the road to HDL mimetics. Curr. Atheroscl. Rep., 10, 405–412. CrossRefGoogle Scholar
  41. Williams, K. J., Feig, J. E., & Fisher, E. A. (2008). Rapid regression of atherosclerosis: insights from the clinical and experimental literature. Nat. Clin. Pract. Cardiovasc. Med., 5(2), 91–102. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  • Anna Cohen
    • 1
  • Mary R. Myerscough
    • 1
  • Rosemary S. Thompson
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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